In his seminal paper on the path integral formulation of quantum mechanics [1]}, Feynman started the introduction of his new theory by pointing out that the law of total probability in classical probability theory must be replaced by a new form of rule. Specifically, in a slightly different notation, the classical law of probability, \(p(c|a)=\sum _bp(c|b)p(b|a)\)  where \(p(y|x)\)  is the probability of obtaining measurement result \(y\)  given measurement result \(x\) , is no longer true in quantum theory, and must be replaced by \(\varphi (c|a)=\sum _b\varphi (c|b)\varphi (b|a)\)  where \(\varphi \)  is a complex number called probability amplitude and related to the classical probability by the Born's rule \(p(y|x)=|\varphi (y|x)|^2\) . From this key idea, Feynman continued to expand the theory that leads to the path integral formulation of quantum mechanics. He also discussed when the new rule of summation over probability amplitude can fall back to the classical law of probability. This is when one “attempts to perform" intermediate measurements that obtain results of all \(b\) . In modern terms, what Feynman means “attempting to perform measurement" here can be understood as the decoherence phenomenon [2]}.
